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Armory is probably the most secure. You can store offline with it. That's what i use. .......... until my ledger nano s arrives. Backordered 2 months. Trezor is backordered too but not as bad.
If you don't want a hardware wallet then definitely get armory

Hi i learning this new technology too, so i heard that paper wallets are the best.

There are hardware wallets that are available. Such as Trezor. (Trezor is sending me one soon and I will review it and post it here on Steemit). That's the most secure because it's a device designed to protect your digital currency.
As for something free, you can get Blockchain.info. It's an app. Pretty secure.Most importantly, keep the currency off of any exchange.

I have always heard to keep it off of the exchanges, it makes sense to me, so that is what I have always done. I just always wonder how safe some of the free online wallets really are, and if I should just pay for the "security" of a hardware wallet. But, then I think those must be fallible at some point too.

Essentially if you keep your private keys, then you should be good. It's the services where they keep the keys that may be unsafe.